JEE Exam > JEE Questions > In a class of 140 students numbered 1 to 140,...
Start Learning for Free
In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :
- a)102
- b)42
- c)1
- d)38
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a class of 140 students numbered 1 to 140, all even numbered studen...
Let n(A ) = number of students opted Mathematics = 70,
n(B) = number of students opted Physics = 46,
n(C) = number of students opted Chemistry = 28,
n(A ∩ B) = 23,
n(B ∩ C) = 9,
n(A ∩ C) = 14,
n(A ∩ B ∩ C) = 4,
Now n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C)
– n(A ∩ C) + n(A ∩ B ∩ C)
= 70 + 46 + 28 – 23 – 9 – 14 + 4 = 102
So number of students not opted for any course
= Total – n(A ∪ B ∪ C)
= 140 – 102 = 38
n(B) = number of students opted Physics = 46,
n(C) = number of students opted Chemistry = 28,
n(A ∩ B) = 23,
n(B ∩ C) = 9,
n(A ∩ C) = 14,
n(A ∩ B ∩ C) = 4,
Now n(A ∪ B ∪ C)
= n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C)
– n(A ∩ C) + n(A ∩ B ∩ C)
= 70 + 46 + 28 – 23 – 9 – 14 + 4 = 102
So number of students not opted for any course
= Total – n(A ∪ B ∪ C)
= 140 – 102 = 38
Most Upvoted Answer
In a class of 140 students numbered 1 to 140, all even numbered studen...
Explanation:
Given, total number of students = 140
Let's find out the number of students who opted each course:
- Mathematics course: All even numbered students
- There are 70 even numbers between 1 to 140
- Therefore, 70 students opted for Mathematics course
- Physics course: Those whose number is divisible by 3
- There are 46 numbers between 1 to 140 which are divisible by 3
- Therefore, 46 students opted for Physics course
- Chemistry course: Those whose number is divisible by 5
- There are 28 numbers between 1 to 140 which are divisible by 5
- Therefore, 28 students opted for Chemistry course
Now, let's find out the number of students who did not opt for any of the three courses:
- Total number of students who opted for at least one course = 70 + 46 + 28 = 144
- Therefore, the number of students who did not opt for any of the three courses = Total number of students - Total number of students who opted for at least one course
- = 140 - 144
- = -4 (which is not possible)
Hence, the correct answer is option 'D' - 38. This means that there must be an error in the given question as it is not possible for the number of students who did not opt for any course to be negative.
Given, total number of students = 140
Let's find out the number of students who opted each course:
- Mathematics course: All even numbered students
- There are 70 even numbers between 1 to 140
- Therefore, 70 students opted for Mathematics course
- Physics course: Those whose number is divisible by 3
- There are 46 numbers between 1 to 140 which are divisible by 3
- Therefore, 46 students opted for Physics course
- Chemistry course: Those whose number is divisible by 5
- There are 28 numbers between 1 to 140 which are divisible by 5
- Therefore, 28 students opted for Chemistry course
Now, let's find out the number of students who did not opt for any of the three courses:
- Total number of students who opted for at least one course = 70 + 46 + 28 = 144
- Therefore, the number of students who did not opt for any of the three courses = Total number of students - Total number of students who opted for at least one course
- = 140 - 144
- = -4 (which is not possible)
Hence, the correct answer is option 'D' - 38. This means that there must be an error in the given question as it is not possible for the number of students who did not opt for any course to be negative.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer?
Question Description
In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer?.
In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer?.
Solutions for In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :a)102b)42c)1d)38Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup